Advertisements
Advertisements
Question
The cylinder of radius 12 cm have filled the 20 cm with water. One piece of iron drop in the stands of water goes up 6.75 cm. Find the radius of sphere piece.
Advertisements
Solution
Radius of cylinder = 12 cm
Height of cylinder = 6.75 cm
Volume of water = πr2h = π x 12 x 12 x 6.75 cm3
Let the radius of iron sphere piece = R cm.
∵ Volume of sphere = volume of water
`4/3` πR3 = π x 12 x 12 x 6.75
R3 = `(π xx 12 xx 12 xx 6.75 xx 3)/(4π)`
R3 = 729
R = `root(3)(729)` = 9 cm.
Hence radius of sphere piece = 9 cm.
RELATED QUESTIONS
A right circular cylinder just encloses a sphere of radius r (see figure). Find
- surface area of the sphere,
- curved surface area of the cylinder,
- ratio of the areas obtained in (i) and (ii).
Find the surface area of a sphere of radius 10.5 cm.
A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base
of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs. 7 per 100
`cm^2`.
What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm?
If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( π = 3.14 )
If the surface area of a sphere is 2826 cm2 then find its volume. ( π= 3.14)
Find the length of the wire of diameter 4 m that can be drawn from a solid sphere of radius 9 m.
Find the radius of the sphere whose surface area is equal to its volume .
A solid, consisting of a right circular cone standing on a hemisphere, is placed upright, in a right circular cylinder, full of water and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer to the nearest cubic centimetre.
A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.
